Actually, it seems, the structures are not 4, but at least 8, as those could be mirrored on the queen side.
For example, a standard d6-e5-f4 black KID chain could be replicated by an e6-d5-c4 chain on the queen side, with white king castling long, etc.
That seems to happen very rarely in practice, though.

But those are only the structures I myself have discovered. I am pretty much certain there are many other ways of trying to handle the engines
easily, they just wait to be discovered by someone.

As said, if Stockfish does not improve by at least 400 elos in the next year or 2, too many humans will start beating it too easily.